A Two-Period Decision Model for Central Bank Digital Currencies and Households

Abstract

Central bank digital currencies (CBDCs) give rise to many possibilities including those of negative interest rates. A two-period decision model is presented between one central bank and one representative household. The central bank applies the Taylor (1993) rule to choose its interest rate. The household allocates its resources strategically to production, consumption, CBDC holding, and non-CBDC holding. The results are determined analytically and illustrated numerically by varying 19 parameter values. Interesting novelties of the article are that the central bank may choose negative CBDC interest rates when the household holds far more CBDC than non-CBDC, for low inflation rates, low real interest rates, low household’s potential production, low weight assigned to inflation in the Taylor (1993) rule, high target inflation rate, and high household’s production parameter. That usually causes the household to decrease its CBDC holding and increase its non-CBDC holding, production and consumption. The central bank may increase its CBDC interest rate to compete with an increasing non-CBDC interest rate if the household’s transaction efficiencies for CBDC and non-CBDC increase, or the household’s transaction efficiency for consumption decreases. Shocks to production, inflation and interest rates are analyzed.